(2x-4)x+7=90

Solution for (2x-4)x+7=90 equation:

(2x-4)x+7=90

We move all terms to the left:

(2x-4)x+7-(90)=0

We add all the numbers together, and all the variables

(2x-4)x-83=0

We multiply parentheses

2x^2-4x-83=0

a = 2; b = -4; c = -83;
Δ = b2-4ac
Δ = -42-4·2·(-83)
Δ = 680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{170}}{2*2}=\frac{4-2\sqrt{170}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{170}}{2*2}=\frac{4+2\sqrt{170}}{4}
$